The present invention relates to automatic equalizers which compensate for the distorting effects of band-limited channels on transmitted data signals.
Automatic equalizers are necessary for accurate reception of high-speed data signals transmitted over band-limited channels with unknown transmission characteristics. The equalizer is generally in the form of a transversal filter in which successive samples of the incoming data signal are multiplied by respective tap coefficients. The resulting products are added together to generate an "equalized" signal which is then demodulated and/or quantized to recover the transmitted data. In addition, an error signal is formed equal to the difference between the equalized signal and a reference signal which represents the transmitted data symbol. The value of the symbol that was transmitted may be known at the receiver, a priori as is the case in many equalizer start-up arrangements. Alternatively, as in the so-called adaptive type of automatic equalizer, the reference signal is derived from the decision made in the receiver (on the basis of the equalized signal value) as to what data symbol was transmitted. In either case, the error signal is used to update the tap coefficient values in such a way as to minimize a measure of the distortion--primarily intersymbol interference--introduced by the channel. The most commonly used error-directed coefficient updating algorithm is the so-called mean-squared error algorithm, which adjusts the tap coefficients so as to minimize the average of the value of the square of the error signal.
Most commercial data receivers, e.g., data modems, incorporate a synchronous, or baud, equalizer in which the received data signal is sampled at a rate equal to the symbol rate. It is, however, possible to use a so-called fractionally-spaced equalizer in which the received signal is sampled at a higher rate. Data decisions, i.e., quantizations of the equalized samples, are still made at the symbol rate. However, the fact that equalization is carried out using a finer sampling interval provides the fractionally-spaced equalizer with significant advantages over its more conventional cousin. Most notable among these is insensitivity to channel delay distortion, including sampling phase errors.
There is, however, at least one significant problem unique to the fractionally-spaced equalizer. In a synchronous equalizer, one set of tap coefficients is clearly optimum, i.e., provides the smallest mean-squared error. By contrast, many sets of coefficient values provide approximately the same mean-squared error in the fractionally-spaced equalizer. As a consequence of this property, the presence of small biases in the coefficient updating processing hardware--such as biases associated with signal value roundoff--can cause at least some of the coefficient values to drift to very large levels, or "blow-up", even though the mean-squared error remains at, or close to, its minimum value. The registers used to store the coefficients or other signals computed during normal equalizer operation can then overflow, causing severe degradation, or total collapse, of the system response.
The prior art--exemplified by G. Ungerboeck, "Fractional Tap-Spacing Equalizers and Consequences for Clock Recovery for Data Modems," IEEE Trans. on Communications, Vol. COM-24, No. 8, August 1976, pp. 856-864--suggests that the problem of coefficient value blow-up can be controlled by introducing one of two alternative auxiliary terms into the conventional updating algorithm. The auxiliary term may be, for example, a predetermined small fraction of the current value of the coefficient being updated. This implements a so-called tap leakage approach. Alternatively, a spectral zero-forcing approach is suggested. Here the auxiliary term is a predetermined small fraction of an alternating-sign sum of the current values of all the coefficients.
Having presented these approaches for controlling coefficient blow-up, the Ungerboeck article further reports that in a computer simulation of a fractionally-spaced equalizer, blow-up actually never occurred, at least when sufficient precision was used in the computations.